An Algebraic Obstruction to Isomorphism of Markov Shifts with Group Alphabets

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Ward, T. B. (1993) An Algebraic Obstruction to Isomorphism of Markov Shifts with Group Alphabets. Bulletin of the London Mathematical Society, 25 (3). pp. 240-246. ISSN 0024-6093

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Abstract

Given a compact group G, a standard construction of a Z2 Markov shift SG with alphabet G is described. The cardinality of G (if G is finite) or the topological dimension of G (if G is a torus) is shown to be an invariant of measurable isomorphism for SG. We show that if G is sufficiently non-abelian (for instance A5, PSL2(F7), or a Suzuki simple group) and H is any abelian group with |H| = |G|, then SG and SH are not isomorphic. Thus the cardinality of G is seen to be necessary but not sufficient to determine the measurable structure of SG.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:48
Last Modified: 15 Dec 2022 02:09
URI: https://ueaeprints.uea.ac.uk/id/eprint/18596
DOI: 10.1112/blms/25.3.240

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